Computer-implemented systems and methods for calculating estimated transaction costs for transactions involving tradable financial products

ABSTRACT

Computer-implemented systems and methods for computing a transaction cost metric for a transaction (or trade order) involving a tradable financial product, such as a FX currency pair. The transaction cost metric can be computed pre-trade and compared to a quoted price for the trade from a dealer to evaluate the quoted price. The computed transaction cost metric, which is based on a slippage premium for the trade order, is based on at least a notional size for the trade order. The slippage premium represents a difference between an effective price at which the trade order is filled and a price for the financial product at inception of the trade order. The transaction cost metric may be computed as an average of a strip of options, where the values of the options are computed using an option pricing formula. The strip of options may comprise one or more options, each with different tenors, where the tenors correspond to the expected time periods for orders to arrive to fill the trade order.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application incorporates by reference in its entirety theconcurrently filed application by Paul Aston, entitledCOMPUTER-IMPLEMENTED SYSTEMS AND METHODS FOR DETERMINING LIQUIDITY CYCLEFOR TRADABLE FINANCIAL PRODUCTS AND FOR DETERMINING FLOW-WEIGHTEDAVERAGE PRICING FOR SAME,” Ser. No. 12/904,436.

BACKGROUND

Financial markets are inherently volatile, characterized by shiftingvalues, risks and opportunities. The prices of individual financialproducts are frequently changing for numerous reasons, including shiftsin perceived value, localized supply/demand imbalances, and pricechanges in other sector investments or the market as a whole. Reducedliquidity adds price volatility and market risk to any contemplatedtransaction, and in the face of this volatility, Transaction CostAnalysis (TCA) has become increasingly important to help firms measurehow effectively both perceived and actual portfolio orders arecompleted.

Several well-conceived TCA frameworks have evolved, but mostly forequities (e.g., stocks). These equity TCA frameworks rely on the marketliquidity information that is available from equity exchanges. Forfinancial products where market liquidity information is not readilyobservable, such as currency, there are few if any TCA solutions.

Currencies are not like exchange-traded assets. The currency market isfragmented, highly decentralized, and trades over-the-counter (OTC).This means there is no single institution that serves as point forliquidity aggregation and information dissemination. Instead, the marketbasically operates as a quasi-centralized network of dealers thatincludes major banks, broker-dealers and electronic communicationsnetworks (ECNs). In the currency market, dealers tend to manage theirown order flows and closely guard them as proprietary information. Sincemost transactions in global foreign exchange are executed as privatebilateral agreements, the terms of these agreements (i.e., transactedprice and volume) are rarely revealed to other market participants. Theresult is a market rife with informational asymmetries, where liquidityis largely hidden from view.

SUMMARY

In one general aspect, the present invention is directed tocomputer-implemented systems and methods for computing a transactioncost metric for a transaction (or trade order) involving a tradablefinancial product, such as a FX currency pair. The transaction costmetric, which is related to what is herein referred to as the “slippagepremium,” can be computed pre-trade and compared to a quoted price forthe trade order from a dealer to evaluate the quoted price. The computedtransaction cost metric is based on at least a notional size for thetrade order and represents a difference between an effective price atwhich the trade order is filled by future arriving complimentary orders(offers for a bid and vice versa) and a price for the financial productat inception of the trade order. The transaction cost metric may becomputed as an average of computed values for a strip of options, wherethe values of the options are computed using an option pricing formula.The strip of options may comprise one or more options, each with adifferent tenor, where the tenors correspond to the expected timeperiods for complimentary orders to arrive to fill the trade order.

These and other advantages of the present invention will be apparentfrom the description below.

FIGURES

Various embodiments of the present invention are described herein belowin conjunction with the following figures, wherein:

FIG. 1 is a block diagram of a computer system for estimatingtransaction costs for a trade involving a tradable financial productaccording to various embodiments of the present invention; and

FIG. 2 is a diagram illustrating a bid-offer spread;

FIG. 3 is a graph showing a hypothetical limit-order book configuration;

FIG. 4 is a graph showing the liquidity-impact function for thehypothetical limit-order book configuration shown in FIG. 3;

FIG. 5 is a graph showing the hypothetical limit-order bookconfiguration of FIG. 3 with no offered inventory;

FIG. 6 is a graph showing slippage premium option strip values as afunction of tenor according to an example of the present invention;

FIG. 7 a-d are graphs showing exemplary potential costs as a function oforder arrival waiting times for different levels of market volatility

FIG. 8 is a flowchart showing a process for computing estimatedtransaction costs for a transaction involving a tradable financialproduct according to various embodiments of the present invention;

FIGS. 9 a-d are graphs showing the average rate of order arrivals, orderarrival waiting times, order flow, and order size throughout the Londonday on the EBS dealing platform;

FIG. 10 a-d show statistics for RIV levels observed in 2009 for EURUSDbetween Jan. 1 and Jul. 21, 2009

FIG. 11 is a diagram of a computer network for a web-based transactioncost calculator according to various embodiments of the presentinvention;

FIG. 12 is a diagram of a computing environment according to variousembodiments of the present invention.

DESCRIPTION

Various non-limiting embodiments of the present disclosure will now bedescribed to provide an overall understanding of the principles of thestructure, function, manufacture, and use of the systems and methodsdescribed herein for transaction costs analysis for trades involving atradable financial product. In the description to follow, the tradablefinancial products are generally foreign currency exchange (FX) pairs(such as Euro-U.S. Dollar (sometimes denominated “EURUSD”)) used in spottrading of foreign currency, although the present invention is not solimited and it should be recognized that the systems and methods of thepresent invention could be used for other types of tradable financialproducts, such as equities (e.g., stock), debt (e.g., bonds), andderivative contracts (futures, options, commodities, etc.). One or moreexamples of these non-limiting embodiments are illustrated in theaccompanying drawings. It will be appreciated that the systems andmethods specifically described herein and illustrated in theaccompanying drawings are non-limiting example embodiments and that thescope of the various non-limiting embodiments of the present disclosureare defined solely by the claims. The features illustrated or describedin connection with one non-limiting embodiment can be combined with thefeatures of other non-limiting embodiments. Such modifications andvariations are intended to be included within the scope of the presentdisclosure.

FX products are typically expressed in pairs, with a left-hand currencyand a right-hand currency, such as EURUSD (Euro—U.S. Dollar), USDJPY(U.S. Dollar—Japanese Yen), GBPUSD (Great Britain Pound—U.S. Dollar),USDCHF (U.S. Dollar—Swiss Franc), and many others. A FX marketparticipant can buy the left-hand currency by selling the right-handcurrency and vice versa. The spot markets for FX products are typicallyover-the-counter (OTC) markets and some spot FX dealing platformspresently exist, such as the EBS and Reuters. A trader receiving anorder from a customer/FX market participant may place the customer'sorder with one of the dealing platforms or some other FX market forexecution.

One of the basic goals of TCA is to model market impact, or the extentto which a particular sized transaction might move price against thebuyer or seller. Typically, to gain an empirical sense of therelationship between order size and market impact, TCA models havefocused mostly on ex-post statistical analyses of observed bid-offerspreads and/or cross-dealer pricing surveys. For the most part, thesetechniques have been successful when analyzing exchange-traded assetssince the critical information needed to conduct TCA (i.e., transactedprice and volume) is readily available from the exchange. However, thisinformation is rarely available in the OTC currency markets and, as aresult, currency TCA techniques need to go beyond traditionalapproaches. One approach is to tackle the problem from first principlesusing a microstructure model of dealer price setting behavior. Dealerprice setting behavior relates directly to the inventory problem ofprocuring liquidity and managing order flows under risk aversion. Thedescription below describes this model in detail and demonstrates howthe model yields, in various embodiments, the seminal Black-Scholes(B-S) options pricing formula as a succinct way to explain transactioncosts and the dynamics of market impact.

One of the fundamental challenges a dealer faces when making a market inFX is the ability to quote competitive prices while managingasynchronous order flows on a continuing basis. This type of marketenvironment is known as a continuous double auction (CDA). Since it isunlikely that mutually compatible buy and sell orders will arrive atexactly the same instant in time, dealers must have a way to warehousepositions in inventory until complimentary orders arrive. To accomplishthis many dealers and dealing platforms employ a limit-order book and aset of trade-order priority rules.

A limit order book may be embodied as a database to record orderinventory. Order inventory can include (i) limit-orders, which areinterests to buy or sell a financial product (e.g., a FX currently pair)at a specified price, (ii) market-orders, which are interests to buy orsell the financial product at the best available price; and (iii) activerisk positions, which occur when a dealer procures liquidity from theirown balance sheet at a specified price. The act of procuring liquidityfor a customer against the dealer's own balance sheet constitutes a formof leveraged lending known as endogenous liquidity. Trade-order priorityrules define how to process newly arriving order flows with orders andpositions already standing in inventory. Trade-order priority rulestypically ensure that all orders execute at the best prices available onthe limit order book.

The most common way to prioritize standing orders for execution is torank them by price on a first-in/first out basis. When orders are rankedin this fashion, the bid-offer inventory on a dealer's limit-order bookwill tend to look like a pair of histograms. FIG. 3 illustrates ahypothetical limit order book. Here, the x-axis measures prices in“pips” and the y-axis shows the amount of liquidity standing at eachprice in millions. In currency markets, the convention is to quote pips( 1/100^(th) of a cent) around the currency's big figure price. Thus, ifEURUSD is quoted as 1.4549/51, this indicates that the inside bid andoffer prices are 1.4549 and 1.4551, respectively, and that the bigfigure price is 1.45. Standing bids are shown in FIG. 3 as the bidsranging from 42 to 49, and standing offers are shown in FIG. 3 as offersranging from 51 to 58. The configuration of these histograms illustratesthe distribution of standing liquidity across various prices on thelimit-order book. Notice that the priority ranking of orders immediatelyreveals the inside (best) bid and offer quotes on the book. In thisexample the inside bid and offer stand at 49/51. Because the mid-priceis defined as the median of the inside bid-offer, the mid-price is 50.The bid-offer spread, as shown in FIG. 2, is the difference between theprevailing inside offer and the prevailing inside bid for the product,with the mid-price at the mid-point between the inside offer and insidebid. The inside bid/offer tend to be the most competitive quotes that adealer will show to the market. In fact, these are typically the onlyprice indications a dealer will reveal to the market. Dealers rarelyreveal information about inventory standing outside their inside quotes.This is why in FIG. 3 the outside liquidity on the limit-order book isshown with hatching. This represents the currency market's hiddenliquidity. The hidden configuration of a dealer's limit-order book playsa structural role in the determination of transaction costs and thebid-offer spread.

The transaction cost identify function represents a dealer's breakevenprofit & loss (P&L) equation. This function relates a dealer's quotedprice, representative of a dealer's revenue in a transaction, to adealer's underlying cost structure for procuring liquidity in atransaction. With loss of generality, a dealer's operational and balancesheet costs are ignored in this framework. One convenient way to look atthis relationship is in terms of the visible and hidden costs of acurrency transaction. A dealer's quoted price may be modeled as:

$\begin{matrix}{{{Quoted}\mspace{14mu}{Price}} = {\underset{{Visible}\mspace{14mu}{Cost}}{\underset{︸}{{{Mid}\mspace{14mu}{Price}} \pm {{.5} \times {Spread}}}} \pm \underset{{Hidden}\mspace{14mu}{Cost}}{\underset{︸}{\left( {{w_{L} \times {Liquidity}\mspace{14mu}{Premium}} + {w_{S} \times {Slippage}\mspace{14mu}{Premium}}} \right)}}}} & (1)\end{matrix}$This perspective relates a quoted price to the prevailing mid-price andthe visible bid-offer spread. The spread, liquidity and slippage premiaare added or subtracted when a dealer quotes an offer price or a bidprice, respectively. The difference between the quoted price and thevisible cost of the transaction is attributable to the hidden cost ofthe transaction, which one can view as the market impact component.

The hidden cost of a transaction can be decomposed further into aliquidity and a slippage premium. The micro-economic origin of thesepremia emanates from a basic inventory problem a dealer faces whenprocuring liquidity in a transaction. When a dealer receives an order,the dealer has two choices as to how to fill it: (1) the dealer canchoose to fill the order out of standing inventory; or (2) the dealercan choose to wait and fill the order against newly arriving order flow.The liquidity premium reflects the cost of filling an order out ofstanding inventory, while the slippage premium represents the expectedcost of filling an order against arriving order flow. Because a dealercan fill an order against both standing inventory and arriving orderflow, the hidden cost of a currency transaction may represent a weightedaverage of the two. Hence, in the transaction cost identify functionw_(L)+w_(S)=1, with both 1≧w_(L)≧0 and 1≧w_(S)≧0.

The particular form of the transaction cost identify function expressedby Equation (1) assumes that all dealers base quoted prices off the samevisible cost; the mid price and visible bid-offer spread. If currenciestraded on a centralized exchange, this would be a valid assumption sincemost exchanges employ a single, official limit-order book. However, thecurrency market is a decentralized, over-the-counter (OTC) market wheredealers manage their own limit-order books on a proprietary basis.

An alternative way to look at a dealer's P&L equation is to relate adealer's quoted price to their own proprietary cost structure.Quoted Price_(offer)=Inside Bid+w _(L)×Full Liquidity Premium+w_(S)×Full Slippage PremiumQuoted Price_(Bid)=Inside Offer−w _(L)×Full Liquidity Premium−w_(S)×Full Slippage Premium  (2)Here, the bid-offer spread subsumes completely into the liquidity andslippage premia.Full Liquidity Premium=Liquidity Premium+SpreadFull Slippage Premium=Slippage Premium+Spread  (3)That rational behind this perspective is that if a dealer wants to offerliquidity, the dealer must acquire the inventory to do so by bidding forit on the open market. In a competitive market, a dealer will bereluctant to pay too much for inventory since this will erode profitmargins if liquidity cannot be offered above a certain price. Hence, adealer's inside bid can be viewed as the reservation price above whichthe dealer is unwilling to acquire inventory, given the dealer's abilityto sell it at a particular price. This logic is reflexive in the sensethat once a dealer acquires inventory at a particular cost, the dealerwill be reluctant to sell it at a loss. Hence, a dealer's inside offercan be viewed as the reservation price below which the dealer isunwilling to dispose of inventory, given its underlying cost.

If the liquidity premium represents the cost of filling an order out ofstanding inventory and the slippage premium represents the expected costof filling an order against arriving order flow, then the bid-offerspread may be endogenously determined by the configuration of a dealer'slimit order book and the characteristics of the dealer's order flow. Tosee this more clearly, define the bid-offer spread in terms of Equation(2)

$\begin{matrix}\begin{matrix}{{Spread} = {{{Quoted}\mspace{14mu}{Price}_{Offer}} - {{Quoted}\mspace{14mu}{Price}_{Bid}}}} \\{= {{{Inside}\mspace{14mu}{Bid}} - {{Inside}\mspace{14mu}{Offer}} + {2 \times}}} \\{\left( {{w_{L} \times {Full}\mspace{14mu}{Liquidity}\mspace{14mu}{Premium}} + {w_{S} \times {Full}\mspace{14mu}{Slippage}\mspace{14mu}{Premium}}} \right)}\end{matrix} & (4)\end{matrix}$Assuming that in a competitive market a dealer always quotes thedealer's inside bid-offer, Equation (4) yields:Spread=w _(L)×Full Liquidity Premium+w _(S)×Full Slippage Premium  (5)Plugging Equation (5) back into Equation (2) yields the identityInside Offer≡Inside Bid+Spread  (6)Combining this result with the definition of the mid-price,Mid Price≡Inside Bid+Inside Offer)/2  (7)shows that Equation (2) communicates exactly the same information asEquation (1); only the underlying frame of reference for pricing changesfrom the visible cost to the inside quotes, which represent a dealer'sreservation prices. These results are now used to demonstrate thattransaction costs can be directly related to the configuration of adealer's limit-order book and the characteristics of order flow.

The relationship between order size and market impact can be traced bythe liquidity-impact function, which measures the VWAC (volume weightedaverage cost) over the depth of the limit-order book in unit increments.The depth of a limit-order book's configuration is the cumulative sum ofstanding liquidity on either side of the book, counting from the insidequotes out. FIG. 4 illustrates the liquidity-impact function for thelimit-order book depicted in FIG. 3. FIG. 4 shows how the VWAC ofbuy/sell orders may increase/decrease as a function of order size. Forinstance, in the example of FIG. 4, the VWAC of all 37 Mn standingoffers (the cumulative standing offers from the example of FIG. 3) is54.6486 pips; 3.6486 pips more than the visible cost of 51-offered.Since the VWAC provides an important basis for computing the dealer'sbreakeven P&L when filling an order against standing inventory, theliquidity impact function can be used to find the dealer's break evenquote for a particular sized transaction. In terms of P&L, this can bewritten as:P&L=±(Quoted Price−VWAC)  (8)where the ± symbol is + when a dealer quotes an offer price (price tosell currency) and − when a dealer quotes a bid price (price to buycurrency), respectively. To compute the liquidity premium, the quotedprice in Equation (8) can be replaced with the right-hand side ofEquation (1), with P&L set to zero and terms rearranged to yield:Liquidity Premium=±(VWAC−(Mid Price±0.5×Spread))  (9)Using the identities in Equations (6) and (7) yields:Liquidity Premium_(Offer)=max{VWAC−Inside Offer,0}Liquidity Premium_(Bid)=max{Inside Bid−VWAC,0}  (10)where the max{ } argument appears because the liquidity premium must benon-negative. Inserting this last result into Equation (1) shows thatwhen filling an order against standing inventory the quoted price iseffectively equal to the VWAC of a dealer's standing inventory:Quoted Price_(Offer)=Inside Offer+Liquidity Premium=VWAC_(Standing Offers)Quoted Price_(Bid)=Inside Bid−Liquidity Premium=VWAC_(Standing Bids)  (11)

The slippage premium may represent the expected cost of filling an orderagainst arriving complimentary order flow (e.g., arriving offers for abid transaction and vice versa). In various embodiments, the slippagepremium can be identified using the same intuition employed to identifythe liquidity premium. However, in this case, because the prices ofnewly arriving orders tend to follow a random walk, the VWAC ofinventory is stochastic. Thus, intuitively, when sourcing liquidity fromarriving order flow, a dealer's quoted price should be consistent withthe expected VWAC of the liquidity supplied.

A dealer may decide to fill an order against arriving order flow forseveral reasons. One reason might be that the depth of availableliquidity in standing inventory is insufficient to complete a particularsized transaction. Consider this scenario: a dealer receives amarket-order to buy 100 Mn of a first currency (say EUR) selling asecond currency (say USD). Given the configuration of the limit-orderbook depicted in the example of FIG. 3, only 37 Mn of standing offersare available. Because the market-bid exceeds the available liquidity ofall standing offers on the limit-order book, the bid will sweep thebook, cleaning all standing offers out of inventory. FIG. 5 depicts thesituation. If the dealer quotes an up-front, firm price for the full 100Mn, then technically the dealer filled the residual amount of 63 Mnagainst his or her own account at the quoted price. This effectivelycreates an active short position on the dealer's balance sheet and thedealer is at risk if prices drift above the quoted price. To cover theshort, the dealer must buy currency in the open market. One way toachieve this is to wait for new offers to arrive on the limit-orderbook. Since the inside bid represents the dealer's reservation pricewhen quoting an offer (Equation (2)), the dealer's perceived risk ishaving to acquire inventory at prices greater than the inside bid. Thisintroduces two important factors into the dealer's price settingbehavior: waiting time and price volatility.

Since orders arrive randomly, the dealer must wait for sufficientliquidity to arrive on the limit order book before the active riskposition can be closed. During this waiting period, the prices ofarriving orders can vary, thereby introducing the risk of slippage.Slippage occurs whenever the VWAC of inventory deviates from thedealer's reservation price. Intuitively, larger orders expose the dealerto greater slippage risk than smaller orders. This is because largerorders require a greater inventory and balance sheet commitment from thedealer which, in turn, translate into a larger active risk positions,longer expected waiting times and greater potential slippage.

The slippage premium may compensate the dealer fairly for this risk.Consider the way new offers can arrive on the limit-order book under thetrade-order priority rules. When market-offers arrive on the limit orderbook, they will be immediately eligible to be matched against thedealer's inside bid. It turns out that when limit-offers arrive on thelimit-order book, they too will be immediately eligible to be matchedagainst the dealer's bid, except in these cases the orders will beexecuted at the maximum of the arriving limit-offer's price or thedealer's inside bid. (Note that market-bids are always eligible to bematched against standing limit-offers. With no offered liquidity on thelimit-order book, all arriving limit-offers are eligible to be matchedagainst the market-bid at the limit-offer price or better. Thus, if alimit-offer arrives at a price less than the inside-bid it is said to bemarketable and executes immediately just like a market order at the bestbid prices greater than or equal to the limit-offer price.) Thus, basedon the trade order priority rules, the lowest price the dealer shouldexpect to pay to acquire liquidity, is the inside bid. (Of course, thedealer may want to pay a lower price but in a competitive market, thedealer's bid must be at least as competitive as the prevailing insidebid in the market if the dealer's bid is to remain prioritized at thefront of the queue. Even if the dealer submitted a limit-bid at a pricelower than the inside bid, the dealer's bid would need to wait until itbecame the priority inside-bid before being executed. This would onlyincrease waiting time and simply replicate the situation above.)

This suggests that, ultimately, the expected VWAC of inventory dependson the prevailing inside quote and underlying order placementdistribution of limit-order prices. In various embodiments, these factscan be exploited to compute the slippage premium via the Black-Scholes(B-S) option pricing formula. Proceeding in the same fashion as before,the problem can be posed in terms of a dealer's expected breakeven P&L.Let p(t) represent the price of an order arriving at time t. As eachorder arrives, the dealer's marginal realized P&L, given their quotedprice, isΠ(t)=±(Quoted Price−p(t))  (12)where Π denotes P&L, and the ± symbol is positive when the dealer quotesan offer and negative when the dealer quotes a bid price, respectively.Replacing the quoted price with the right-hand side of the Equation (2),setting P&L to zero, and rearranging terms, the realized slippageassociated with an order arriving at time t can be obtained:Slippage_(Offer)(t)=max{p(t)−Inside Bid,0}Slippage_(Bid)(t)=max{Inside Offer−p(t),0}  (13)Since the price of each arriving order can be considered a randomvariable, the dealer may calibrate the dealer's slippage premium to theexpected slippage associated with each arriving order. Hence, for eacharriving order the dealer may seek to find:Full Slippage Premium_(Offer)(t)=E[max{p(t)−Inside Bid,0}]Full Slippage Premium_(Bid)(t)=E[max{Inside Offer−p(t),0}]  (14)Assuming that p(t) follows geometric Brownian motion, Equation (14)suggests that the full slippage premium can be computed as the price ofa European option struck at the inside quote, whose value can becomputed using the Black-Scholes (B-S) option pricing formula by settingthe spot price equal to the mid-price and the strike price equal to theappropriate inside quote. More details regarding the B-S pricing formulamay be found in Hull, Options, Futures, and Other Derivatives, PrenticeHall, 6^(th) Ed. (2006), Chap. 13, which is incorporated herein byreference. According to various embodiments, therefore, the fullslippage premium for an order arriving at time t can be obtained asfollows:Full Slippage Premium_(Offer)(t)=Mid Price×e ^(−ft) N(d ₁)−Inside Bid×e^(−rt) N(d ₂)Full Slippage Premium_(Bid)(t)=Inside Offer×e ^(−rt) N(−d ₂)−Mid Price×e^(−ft) N(−d ₁)  (15)where

${d_{1} = \frac{{\ln(m)} + {\left( {r - f + {{.5}\sigma^{2}}} \right)t}}{\sigma\sqrt{t}}},{d_{2} = {d_{1} - {\sigma\sqrt{t}}}},{m = {{Mid}\mspace{14mu}{{Price}/{Inside}}\mspace{14mu}{Quote}}},$σ is the volatility, and r is an applicable risk free interest rate forthe right-hand side currency and f is an applicable risk free interestrate for the left-hand side currency. Since in most TCA applications twill tend to be less than 1.6×10⁻⁴ and r−f will tend to be relativelysmall, the terms involving e^(−rt) and e^(−ft) can usually be set toequal 1 and r−f can be set to zero. In other embodiments, a price otherthan the mid-price may be used as the strike price in the B-S pricingformula.

Since the notional size N of a single arriving trade order may not besufficient to complete a transaction, a dealer may need to wait for asequence of orders to arrive in order to acquire enough liquidity tocover an active risk position in inventory. In various embodiments, theslippage premium is computed from a strip of multiple B-S options, eachoption having a different tenor. If the notional size of a trade orderis N, and the average size of each newly arriving order is q, then theexpected number of complimentary orders required to complete atransaction is

$\begin{matrix}{K = \left\lceil \frac{N}{q} \right\rceil} & (16)\end{matrix}$where the ceiling function ┌•┐ means round N/q up to the next largestinteger.

Since orders arrive at random, order arrivals can be described using aPoisson process. If the mean of a Poisson process λ represents theaverage rate of order arrivals per unit time (e.g. 5 orders per second,300 orders per minute, etc. . . . ), it can be shown from the waitingtime distribution of the Poisson that the expected waiting time for thenext order to arrive is

$\begin{matrix}{{E\lbrack w\rbrack} = \frac{1}{\lambda}} & (17)\end{matrix}$If {t_(k)}_(k=1) ^(K) represents a sequence of order arrival times,t₁<t₂ . . . <t_(K), observed until enough liquidity is sourced fromarriving order flow to complete a transaction, then the expected valueof the k′th tenor in the strip of B-S slippage premium options is

$\begin{matrix}{t_{k} = {{E\left\lbrack w_{k} \right\rbrack} = \frac{k}{\lambda}}} & (18)\end{matrix}$for k=1, . . . , K. This implies that the full slippage premium may becomputed as a weighted average of each slippage premium option in thestrip

$\begin{matrix}{{{{Full}\mspace{14mu}{Slippage}\mspace{14mu}{Premium}_{Offer}} = {N^{- 1}{\sum\limits_{k = 1}^{K}\;{\hat{q} \times {Full}\mspace{14mu}{Slippage}\mspace{14mu}{{Premium}_{Offer}\left( t_{k} \right)}}}}}{{{Full}\mspace{14mu}{Slippage}\mspace{14mu}{Premium}_{Bid}} = {N^{- 1}{\sum\limits_{k = 1}^{K}\;{\hat{q} \times {Full}\mspace{14mu}{Slippage}\mspace{14mu}{{Premium}_{Bid}\left( t_{k} \right)}}}}}} & (19)\end{matrix}$where {circumflex over (q)} equals q for k=1, . . . , K−1 andmin{N−(K−1)q,q} for k=K. Inserting this last result into Equation (2)shows that when filling an order against newly arriving order flow thequoted price is effectively equal to the inside quote, plus the expectedslippage computed from a strip of B-S options:Quoted Price_(Offer)=Inside Bid+Full Slippage Premium_(Offer)Quoted Price_(Bid)=Inside Offer−Full Slippage Premium_(Bid)  (20).

From the dealer's perspective:Quoted Price_(Offer)=Inside Bid+w _(L)×Full Liquidity Premium_(Offer) +w_(S)×Full Slippage Premium_(Offer)Quoted Price_(Bid)=Inside Offer−w _(L)×Full Liquidity Premium_(Bid) −w_(S)×Full Slippage Premium_(Bid)  (21)Unfortunately, in practice this result is only useful for a dealer,since the information required to estimate the full liquidity premium,i.e. the particular configuration of the dealer's limit order book, isproprietary and not transparent. However, for Equation (21) to bebroadly applicable, all that is required is to garner an estimate of thefull liquidity premium. Recall that

$\begin{matrix}\begin{matrix}{{{Full}\mspace{14mu}{Liquidity}\mspace{14mu}{Premium}_{Offer}} = {{{Liquidity}\mspace{14mu}{Premium}_{Offer}} +}} \\{Spread} \\{= {{\max\left\{ {{{VWAC} - {{Inside}\mspace{14mu}{Offer}}},0} \right\}} +}} \\{Spread} \\{= {\max\left\{ {{{VWAC} - {{Inside}\mspace{14mu}{Bid}}},0} \right\}}}\end{matrix} & (22) \\\begin{matrix}{{{Full}\mspace{14mu}{Liquidity}\mspace{14mu}{Premium}_{Bid}} = {{{Liquidity}\mspace{14mu}{Premium}_{Bid}} +}} \\{Spread} \\{= {{\max\left\{ {{{{Inside}\mspace{14mu}{Bid}} - {VWAC}},0} \right\}} +}} \\{Spread} \\{= {\max\left\{ {{{{Inside}\mspace{14mu}{Offer}} - {VWAC}},0} \right\}}}\end{matrix} & \;\end{matrix}$This implies thatE[Full Liquidity Premium_(Offer) ]=E[max{VWAC−Inside Bid,0}]E[Full Liquidity Premium_(Bid) ]=E[max{Inside Offer−VWAC,0}]  (23)In other words, the expected value of the liquidity premium can bedetermined directly from the same B-S methodology used to compute theslippage premium. This suggests that the results obtained in Equations(15) through (20) can serve as the practical basis for a TCA framework.Supporting this notion is the fact that standing orders on thelimit-order book originated from arriving order flow in the first place.Thus, the VWAC configuration of the limit-order book can be expected toconverge asymptotically to the underlying distribution of limit-orderprices. As long as one assumes that the limit-order placementdistribution is characterized by a mean and a variance, the Principle ofMaximum Entropy suggests that the Gaussian normal distribution can serveas the most representative and least committal distributional form toexplain the VWAC of dealer inventory.

In various embodiments, the transaction costs are characterized relativeto the mid-price. This helps to facilitate TCA comparisons between bothbuy and sell transactions and across currencies. In addition,standardizing the B-S transaction cost equation around the mid-pricehelps to reveal the three fundamental sources of transaction costs: thevisible bid-offer spread, the size of an order relative to the depth ofmarket liquidity and price volatility. To standardize the B-Stransaction cost equation around the mid-price, start by dividing bothsides of Equation (15) by the mid-price, yielding:

$\begin{matrix}{\mspace{79mu}{{\frac{{Full}\mspace{14mu}{Slippage}{\mspace{11mu}\;}{{Premium}_{Offer}(t)}}{{Mid}\mspace{14mu}{Price}} = {{N\left( d_{1} \right)} - {\left( {1 - {S/2}} \right) \times {N\left( d_{2} \right)}}}}{\frac{{Full}\mspace{14mu}{Slippage}{\mspace{11mu}\;}{{Premium}_{Bid}(t)}}{{Mid}\mspace{14mu}{Price}} = {{\left( {1 + {S/2}} \right) \times {N\left( {- d_{2}} \right)}} - {N\left( {- d_{1}} \right)}}}}} & (24)\end{matrix}$Then insert this result into Equation (20) to obtain:

$\begin{matrix}{\begin{matrix}{\;{{\frac{{Quoted}\mspace{14mu}{Price}_{Offer}}{{Mid}\mspace{14mu}{Price}} - 1} = {\frac{{Inside}\mspace{14mu}{Bid}}{{Mid}\mspace{14mu}{Price}} +}}} \\{\frac{{Full}\mspace{14mu}{Slippage}{\mspace{11mu}\;}{Premium}_{Offer}}{{Mid}\mspace{14mu}{Price}} - 1} \\{= {{- \frac{S}{2}} +}} \\{N^{- 1}{\sum\limits_{k = 1}^{K}\;{\hat{q}\begin{bmatrix}{{N\left( {d_{1}\left( t_{k} \right)} \right)} -} \\{\left( {1 - \frac{S}{2}} \right) \times {N\left( {d_{2}\left( t_{k} \right)} \right)}}\end{bmatrix}}}}\end{matrix}\begin{matrix}{{\frac{{Quoted}\mspace{14mu}{Price}_{Bid}}{{Mid}\mspace{14mu}{Price}} - 1} = {\frac{{Inside}\mspace{14mu}{Offer}}{{Mid}\mspace{14mu}{Price}} -}} \\{\frac{{Full}\mspace{14mu}{Slippage}{\mspace{11mu}\;}{Premium}_{Bid}}{{Mid}\mspace{14mu}{Price}} - 1} \\{= {\frac{S}{2} - {N^{- 1}{\sum\limits_{k = 1}^{K}\;{\hat{q}\begin{bmatrix}{\left( {1 + \frac{S}{2}} \right) \times} \\{{N\left( {- {d_{2}\left( t_{k} \right)}} \right)} - {N\left( {- {d_{1}\left( t_{k} \right)}} \right)}}\end{bmatrix}}}}}}\end{matrix}} & (25)\end{matrix}$In Equations (24) and (25), the term S denotes the bid-offer spreadexpressed as a percentage of the mid-price (i.e. S=(Inside Offer−InsideBid)/Mid Price), which enables the terms d₁(t_(k)) and d₂(t_(k)) to bewritten as

${d_{1}\left( t_{k} \right)} = \frac{{- {\ln\left( {1 \mp {S/2}} \right)}} + {{.5}\sigma^{2}t_{k}}}{\sigma\sqrt{t_{k}}}$(the ∓ symbol applying to quoted offers and bid prices, respectively)and d₂=d₁−σ√{square root over (t_(k))}. In Equation (24) the termsinvolving r and f have been ignored as explained above.

Equation (25) expresses the full cost of a transaction in terms of howmuch the quoted price deviates from the mid-price, on a percentagebasis. Equation (25) shows that the full cost of a transaction isattributable to three core factors: (1) the visible bid-offer spread, S,expressed as a percentage of the mid-price; (2) the relative size of anorder compared to the depth of market liquidity, given by the sequenceof expected order arrival waiting times {t_(k)}_(t=1) ^(K) obtained fromEquations (16) through (18); and (3) the expected volatility prevailingover the order arrival waiting period. Each of these parameters can beestimated ex-ante, which means that a transaction cost metric (e.g.,Equation (25)) can be computed pre-trade, rather than waiting until atransaction is complete. For example, the transaction cost metric(Equation 25) could be computed pre-trade using trade order inceptionmarket conditions.

By standardizing the B-S transaction cost equation around the mid-price,the burden of explicitly identifying the inside bid or offer prevailingin the market is also alleviated, which in turns eliminates the need toexplicitly identify the prevailing mid-price. As long as a visiblespread is assumed, Equation (25) permits the inside bid/offer to beimplicitly accounted for. This is quite valuable because in the OTCcurrency market, bid-offer quotes always represent dealer quoted prices;market participants technically never see a dealer's inside quotes. Byexpressing the inside quotes in terms of a percentage spreadadded/subtracted from the mid-price, any hidden reservation price can beaccommodated with consistent results in the TCA framework. In fact, bysetting the spread to zero, it is assumed that all dealers share themid-price as a reservation price and that a dealer's quoted price alwaysreflects the mid-price plus/minus a slippage premium to cover thedealer's risk for procuring liquidity in the transaction. This is whythe first term on the right hand side of Equation (25) subtracts or addsS/2 (depending on whether the trade is an offer or bid); since the fullslippage premium computed by B-S includes the full spread, one half thespread must be discounted from the quoted price if the standardreference is the mid-price.

Equation (25) can be further rewritten if the assumption of midreference pricing (i.e. zero spread) is assumed:

$\begin{matrix}{{\frac{{Quoted}\mspace{14mu}{Price}_{Offer}}{{Mid}\mspace{14mu}{Price}} - 1} = {{N^{- 1}{\sum\limits_{k = 1}^{K}\;{\hat{q}\left\lbrack {{2\;{N\left( {{.5} \times \sigma\sqrt{t_{k}}} \right)}} - 1} \right\rbrack}}} = {\frac{{Quoted}\mspace{14mu}{Price}_{Bid}}{{Mid}\mspace{14mu}{Price}} - 1}}} & (26)\end{matrix}$where use is made of the fact that N(−x)=1−N(x). Equation (26) showsthat when pricing relative to the mid price, transaction costs are fullyattributable to a slippage premium to cover a dealer's risk of procuringinventory. This slippage premium ultimately calibrated to thecharacteristics of order flow, which can be described succinctly byexpected order arrival waiting times and expected price volatility.Equation (26) effectively permits one to compute transaction costsex-ante, and to compute precise market impact assessments for orders ofvarying size given an assumed order flow rate and volatility.

FIG. 1 is a diagram of a computer system 10 for computing a transactioncost metric that can be used to assess a quoted price for a trade orderinvolving a tradable financial product (such as a FX pair) according tovarious embodiments of the present invention. The computed transactioncost metric, which could be computed using Equations (25) and/or (26),for example, can be compared pre-trade to a dealer's quoted price forthe trade order to assess whether the dealer's price is fair given thesize of the order and the prevailing market conditions. Beforedescribing the mechanisms for computing the metric, a brief descriptionof the computer system 10 is provided. The computer system 10 maycomprise one or more networked, electronic computer devices, such asservers, personal computers, workstations, mainframes, laptops, and/orhandheld computing devices. The computer device(s) may comprise one ormore processors 12 and one or more computer memories 14. Theprocessor(s) 12 and the computer memory(ies) 14 may comprise integratedcircuits, for example. In one embodiment, the processor(s) 12 and thecomputer memory(ies) 14 may comprise separate integrated circuits,although in other embodiments they may be combined in a commonintegrated circuit. For convenience, only one processor 12 and only onememory 14 are shown in FIG. 1. The processor 12 may have one or multiplecores. The memory 14 may comprise primary computer memory, such as aread only memory (ROM) and/or a random access memory (e.g., a RAM). Thememory could also comprise secondary memory, such as magnetic or opticaldisk drives or flash memory, for example.

As shown in FIG. 1, the memory 14 may comprise a transaction costscomputation module 16. The transaction costs computation module 16 maycomprise computer software instructions that when executed by theprocessor 12 cause the processor 12 to compute the transaction costmetric for a trade order involving a tradable financial product, such asa FX currency pair, using the techniques described herein. Thetransaction costs computation module 16 may compute the transaction costmetric based on inputs regarding the trade order and/or data stored in acomputer database 20. The database 20 may store, among other things,tick data received from one or more market data sources 22. The tickdata may comprise time-stamped price data published by the market datasources 22. The tick data may comprise: (1) time-stamped indicativeprice quotes (i.e., limit orders to buy or sell the financial product ata specified price) and (2) time-stamped data regarding completedtransactions involving the financial product. For FX, time-stamped dataregarding completed transactions are often referred to as “paid-given”data, which indicates the price paid or given for an executed FXtransaction involving a currency pair.

According to various embodiments, inputs needed to compute thetransaction cost metric may comprise: (i) the type of order (e.g., bidor offer); (ii) the notional size of the order (N); (iii) the averagerate of order arrivals per unit time (A); (iv) the assumed volatility(c); and (v) the assumed bid-offer spread. These values may be input bya user (e.g., a FX market participant) to the computer system 10,calculated by the computer system 10 using data from the database 20,and/or default values could be used. For example, a user (e.g., a FXmarket participant) may input the type of trade order and the notionalsize of the order (N) via a computer network, such as described below inconnection with FIG. 11. The computer system 10 could estimate theaverage rate of order arrivals per unit time (λ) based on the tick datain the database 20 or a default value could used or the user could inputa desired λ. Similarly, computer system 10 could estimate the assumedvolatility (σ) based on the tick data in the database 20, a defaultvalue could be used, or the user could input a desired σ. Also, the usercould input an applicable bid-offer spread or tick data could be used todetermine the applicable bid-offer spread.

FIG. 8 is a flowchart of a process executed by the computer system 10(such as when executing the code of the transaction cost computationmodule 16) for computing the transaction cost metric. Although the stepsof FIG. 8 are shown in a particular serialized order, some of the stepsmay be performed in various orders and/or at the same time. Theillustrated process starts at step 40, where the number of complimentaryorders K required to complete the order is computed. K may be computedper Equation (16) above as

$K = {\left\lceil \frac{N}{q} \right\rceil.}$The transaction cost metric may be computed, as described below, as anaverage value of a strip of K options. Next, at step 42, the tenorst_(k) of the K options are computed. The tenors t_(k) may be computedusing Equation (18) above as

${t_{k} = \frac{k}{\lambda}},$where t_(k) is the tenor of the k^(th) option in the strip, k=1, . . . ,K.

If the volatility σ needs computed, it may be computed at step 44. Thevolatility can be computed using any suitable statistical technique.FIGS. 9 a-9 d present the average rate of order arrivals, order arrivalwaiting times, order flow and order size observed throughout the Londonday on the EBS™ dealing platform. For FX, as can be seen from FIG. 9 b,the expected waiting time for an order arrival is typically less than aminute. This can make volatility estimation challenging because there isno implied volatility market for such ultra-short dated tenors, andstatistical estimates can be highly inaccurate due to the small andvariable order arrival sample sizes that carry price information.Therefore, according to various embodiments, range implied volatility(RIV) can be used to estimate the ultra-short term volatility. RIV is aparametric estimate of the standard normal deviation that is consistent,up to a specified confidence level, with an observed high/low pricerange observed over an intra-period time interval. RIV (denoted σ_(RIV))may be defined as:

$\begin{matrix}{\sigma_{RIV} = {{\frac{R}{2\; z_{\alpha}}\sqrt{h}} = {\frac{{\ln({HighPrice})} - {\ln({LowPrice})}}{2\; z_{\alpha}}\sqrt{h}}}} & (26)\end{matrix}$where R represents the expected intra-period price range that might beobserved over a short-term time interval. As shown above, R may bedefined as the log-difference between the high price and the low pricethat might be observed during the time interval. The variable z_(α)represents a standard normal value, associated with a confidencepercentile α, and h denotes the number of waiting periods of duration tthat there are per year, for example. The above equation is are-arrangement of the well-known standard “z-score” (i.e., z=(x−μ)σ⁻¹),where the value of a random variable x is normalized in terms of thestandard normal distribution. For example, to find the RIV that would beconsistent with a given high/low price range with a 99% confidence, zwould be chosen to be z≅2.58. If the time interval for this high/lowprice range is one minute, then h=368,640 (i.e., the number of minutesper year, 256 trading days×24 hours/day×60 minutes/hr).

One benefit of using the RIV measure is that estimates of volatility canbe obtained using either empirical data or a purely subjectiveviewpoint. FIGS. 10 a through 10 d show the RIV levels observed in 2009for EURUSD between Jan. 1 and Jul. 21, 2009. To compute these RIVs, invarious embodiments, the observed price range over each minute in everyday of the data sample can be isolated. The data in each particularminute can be pooled and the median, mean, 75th percentile and maximumof the values for that particular minute can be computed. The resultingprice range statistics can then used to compute the RIV over each minuteof the London trading day. Notice how the RIV cycles throughout the day,rising and falling as market liquidity increases and decreases.Comparing FIGS. 10 a through 10 d to FIGS. 9 a through 9 d shows thatRIVs are low when order flow is slow. The rationale behind thisphenomenon is that fewer orders mean fewer price messages, implying thatthe range of price changes that can be observed over a given minute ismore likely to be constrained. To picture why this would be so, imagineeach arriving order containing a message with information about whetherprices should rise and fall. If no orders arrive during the period,prices cannot change, so the high and low prices would be equal duringthe period. In this situation both the intra-period price range and RIVwould be zero. With a single order arrival, prices can only move up ordown once. To produce a big price move, the information contained inthat single order's message would need to be unusual. However, when manyorders arrive, prices have the chance to move up and down many times,effectively describing a random-walk diffusion process. The RIVimplicitly measures the breadth and dispersion of this diffusionprocess.

Returning to FIG. 8, at step 50, the value of each option in the stripof K options may be computed using a B-S option pricing formula. Invarious embodiments, as described above, the option values may bereferenced to the mid-price. For example, the strike price used in theB-S pricing formula may be an applicable inside price for the financialproduct at order inception (e.g., inside bid or offer), and the spotprice may be the mid-price for the financial product at order inception,although in other embodiments different selections for the strike and/orspot prices may be used to compute the option values. The option valuescan be computed at step 50 using Equations (15) or (24) described above.Next, at step 52, the transaction cost metric (e.g., the slippagepremium) may be computed based on the computed values for each of the Koptions in the strip. For example, the transaction cost metric may becomputed as a weighted average of the computed option values, asdescribed above. The transaction cost metric may be computed in variousembodiments using either Equation (25) or Equation (26) described above.

In many cases order flow can be quite difficult to measure. This is truefor many emerging market currencies. Even for the most liquid developedmarket currencies, estimates of order flow obtained from a particularplatform may not be fully representative of the order flows in themarket as a whole. In these situations, measuring the characteristicwaiting time of a transaction can yield valuable information about orderflows. The characteristic waiting time of a transaction measures theexpected amount of time it would take to fully complete a transaction ofa given size. It is defined as

$\begin{matrix}{{E\left\lbrack \hat{W} \right\rbrack} = {\left\lceil \frac{N}{q} \right\rceil\lambda^{- 1}}} & (27)\end{matrix}$where N represents the notional amount of the transaction; q representsthe average order size; and λ the order arrival rate. The bracketnotation ┌x┐ denotes the ceiling function, which says round x to thenext highest integer. For example, assume that it takes fifty (50)seconds to complete an order for USD 100 Mn equivalent of currency andwe wish to determine the rate of order flow that would be consistentwith this result. Assuming that q=1, λ=120 Mn orders per minute (USD 100Mn divided by 5/6 minutes).

FIGS. 7 a through 7 d show that the slippage premium is both timesensitive and risk sensitive, which is an intuitive result that stemsfrom options pricing theory. In fact, currency transaction costs possessthe same price sensitivity characteristics as options, including thetaand vega. Theta measures the change in an option's value with respect tothe tenor and vega measures the change in an option's value with respectto volatility. An important corollary to this last observation is that:increased waiting time to complete an order increases transaction coststhrough slippage; a cost that will increase as a function of marketrisk. Practitioners should be aware of this fact when breaking up ordersinto smaller size. Although this practice may alleviate the liquidityimpact of an order, it simply substitutes slippage for liquidity impact.The TCA described herein indicates that practitioners should carefullyverify the cost-benefit of breaking up orders to ensure that the cost ofliquidity impact exceeds the cost of slippage.

By observing the average number of order arrivals per unit time (FIG. 9a), the expected waiting time for an order to arrive can be computedusing

${E\lbrack W\rbrack} = {\frac{1}{\lambda}.}$By monitoring the average size of arriving orders, Equation (16) can beused to derive the expected number of orders that will be required tocomplete a particular size transaction. Equation (18) can then be usedto derive the tenors in the strip of options needed to compute theslippage premium.

In various embodiments, the transaction cost metric may be provided inresponse to a request from a market participant. For example, in variousembodiments, a web site may provide a user interface for a marketparticipant to enter particulars about a proposed trade order for afinancial product, such as type of trade, product, and trade size. FIG.11 shows an embodiment where a market participant 80 may place a requestto calculate the transaction cost metric via a web-based user interface.The web-based user interface may be hosted by one or more web servers82. The market participant 80 may connect to the web server 82 via adata communications network 84, such as the Internet or some othersuitable data communications network. The web pages served by the webserver 82 may allow the market participant 80 to specify the particularsfor the proposed trade, including: (i) the financial product (e.g.,currency pair for spot FX trade); (ii) the type of trade (buy or sell);and (iii) the notional order size. As described above, the marketparticipant could also, in various embodiments, specify the assumedvolatility (σ), the order arrival rate (λ), and the bid-offer spread. Invarious embodiments, once the relevant information for the trade isentered via the web-based user interface, the web server 82 (or someother computer system 10 in communication with the web server 82) maycompute the transaction cost metric, such as Equation (25) or (26), Themarket participant 80 can evaluate a dealer quoted price for the tradeusing the computed transaction cost metric, the value for which may betransmitted from the web server 82 to the market participant 80 via thenetwork 84.

FIG. 12 and the following discussion are intended to provide a briefgeneral description of a suitable computing environment in which thedescribed embodiments of the computer system 10 may be implemented. Itshould be understood, however, that handheld, portable, and othercomputing devices and computing objects of all kinds are contemplatedfor use in connection with the described embodiments. FIG. 12illustrates one example of a suitable computing system environment 1000in which the described embodiments may be implemented, such as for thecomputer system 10. Although as made clear above, the computing systemenvironment 1000 is only one example of a suitable computing environmentand is not intended to suggest any limitation as to the scope of use orfunctionality of the described embodiments. Neither should the computingenvironment 1000 be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theoperating computing environment 1000. With reference to FIG. 12, oneembodiment of a system for implementing the described embodimentscomprises a general-purpose computing device in the form of a computersystem 1100. Components of the computer system 1100 may comprise aprocessing unit 1200, a system memory 1300, and a system bus 1210 thatcouples various system components including the system memory 1300 tothe processing unit 1200. The system bus 1210 may be any of severaltypes of bus structures including a memory bus or memory controller, aperipheral bus, and a local bus using any of a variety of busarchitectures. By way of example, and not limitation, such architecturesinclude Industry Standard Architecture (ISA) bus, Micro ChannelArchitecture (MCA) bus, Enhanced ISA (EISA) bus, Video ElectronicsStandards Association (VESA) local bus, and Peripheral ComponentInterconnect (PCI) bus (also known as Mezzanine bus).

The computer system 1100 generally comprises a variety of computerreadable media. Computer readable media can be any available media thatcan be accessed by the computer system 1100 and includes both volatileand nonvolatile media, removable, and non-removable media. Computerstorage media includes volatile and nonvolatile, removable, andnon-removable media implemented in any method or technology for storageof information such as computer readable instructions, data structures,program modules, or other data. The tick data may be stored innonvolatile memory of the computer system 1100. Computer storage mediaincludes, but is not limited to, Random Access Memory (RAM), Dynamic RAM(DRAM), Double-Data-Rate DRAM (DDRAM), Synchronous DRAM (SDRAM), StaticRAM (SRAM), Programmable ROM (PROM), Read Only Memory (ROM),Electrically Erasable Programmable Read Only Memory (EEPROM), flashmemory, polymer memory such as ferroelectric polymer memory, ovonicmemory, phase change or ferroelectric memory,silicon-oxide-nitride-oxide-silicon (SONOS) memory, Compact Disk ReadOnly Memory (CDROM), Compact Disc-rewritable (CDRW) Digital VersatileDisks (DVD) or other optical disk storage, magnetic cassettes, magnetictape, magnetic disk storage or other magnetic storage devices, or anyother medium which can be used to store the desired information andwhich can be accessed by the computer system 1100. It is worthy to notethat some portion or the entire computer storage medium may be includedin other elements of the apparatus computer system 1100. For instance,some or all of computer storage medium may be included on the sameintegrated circuit or chip with elements of the computer system 1100(e.g., processing unit 1200). Alternatively, some portion or the entirecomputer storage medium may be disposed on an integrated circuit orother medium (e.g., a hard disk drive) that is external.

The system memory 1300 includes computer storage media in the form ofvolatile and/or nonvolatile memory such as ROM 1310 and RAM 1320. Abasic input/output system 1330 (BIOS), containing the basic routinesthat help to transfer information between elements within the computersystem 1100, such as during start-up, is typically stored in the ROM1310. The RAM 1320 typically contains data and/or program modules thatare immediately accessible to and/or presently being operated on by theprocessing unit 1200. By way of example, and not limitation, FIG. 6illustrates an operating system 1340, one or more application programs1350, other program modules 1360, and program data 1370.

The computer system 1100 also may comprise otherremovable/non-removable, volatile/nonvolatile computer storage media. Byway of example only, FIG. 6 illustrates a hard disk drive 1410 thatreads data from or writes data to non-removable, nonvolatile magneticmedia, a magnetic disk drive 1510 that reads data from or writes data toa removable, nonvolatile magnetic disk 1520, and an optical disk drive1550 that reads data from or writes data to a removable, nonvolatileoptical disk 1560, such as a CD ROM, CDRW or other optical media. Otherremovable/non-removable, volatile/nonvolatile computer storage mediathat can be used in the example operating environment include, but arenot limited to, magnetic tape cassettes, flash memory cards, digitalversatile disks, digital video tape, solid state RAM, solid state ROM,and the like. The hard disk drive 1410 is typically connected to thesystem bus 1210 through a non-removable memory interface such asinterface 1400, and magnetic disk drive 1510 and optical disk drive 1550are typically connected to the system bus 1210 by a removable memoryinterface, such as interface 1500.

The drives and their associated computer storage media discussed aboveand illustrated in FIG. 6 provide storage of computer readableinstructions, data structures, program modules, and other data for thecomputer system 1100. In FIG. 6, for example, the hard disk drive 1410is illustrated as storing an operating system 1440, one or moreapplication programs 1450, other program modules 1460, and program data1470. Note that these components can either be the same as or differentfrom the operating system 1340, the one or more application programs1350, the other program modules 1360, and the program data 1370. Theoperating system 1440, the one or more application programs 1450, theother program modules 1460, and the program data 1470 are givendifferent numbers here to illustrate that, at a minimum, they aredifferent copies. A user may enter commands and information into thecomputer system 1100 through input devices such as a keyboard 1620 andpointing device 1610, commonly referred to as a mouse, trackball, ortouch pad, and a scanner 1490. Other input devices (not shown) mayinclude a microphone, joystick, game pad, satellite dish, or the like.These and other input devices are often connected to the processing unit1200 through a user input interface 1600 that is coupled to the systembus 1210, but may be connected by other interface and bus structures,such as a parallel port, game port or a universal serial bus (USB). Adisplay device 1910 or other type of display device is also connected tothe system bus 1210 via an interface, such as a video interface 1900,which may in turn communicates with video memory (not shown). Inaddition to the display device 1910, computer systems also may includeother peripheral output devices such as speakers 1970 and a printer1960, which may be connected through an output peripheral interface1950.

The computer system 1100 may operate in a networked or distributedenvironment using logical connections to one or more remote computers,such as a remote computer 1800. The remote computer 1800 may be apersonal computer, a server, a router, a network PC, a peer device orother common network node, and typically includes many or all of theelements described above relative to the computer system 1100, althoughonly a memory storage device 1810 has been illustrated in FIG. 6. Thelogical connections depicted in FIG. 6 include a local area network(LAN) 1710 and a wide area network (WAN) 1730, but may also includeother networks/buses. Such networking environments are commonplace inhomes, offices, enterprise-wide computer networks, intranets, and theInternet.

When used in a LAN networking environment, the computer system 1100 isconnected to the LAN 1710 through a network interface or adapter 1700.When used in a WAN networking environment, the computer system 1100generally includes a modem 1720 or other means for establishingcommunications over the WAN 1730, such as the Internet. The modem 1720,which may be internal or external, may be connected to the system bus1210 via the user input interface 1600, or other appropriate mechanism.In a networked environment, program modules depicted relative to thecomputer system 1100, or portions thereof, may be stored in the remotememory storage device. By way of example, and not limitation, FIG. 6illustrates one or more remote application programs 1850 as residing onthe memory device 1810. It will be appreciated that the networkconnections shown are non-limiting examples and other means ofestablishing a communications link between the computers may be used.

According to various embodiments, the present invention is directed to acomputer system for computing a transaction cost metric for a tradeorder involving a tradable financial product. The transaction costmetric may be the metrics of Equations (25) and/or (26) above, ormodifications thereof. The computer system comprises at least oneprocessor and at least one memory unit in communication with the atleast one processor. The at least one memory unit stores instructionsthat when executed by the at least one processor cause the at least oneprocessor to: (1) compute a number of complimentary orders K required tocomplete the trade order based on a notional size N for the trade order,where K≧1; (2) compute values for each option in a strip of K optionsusing an option pricing formula, where each of the K options has adifferent tenor, and where respective tenors for each of the K optionsin the strip correspond to expected waiting times for each of the numberof complimentary orders K required to fill the trade order; and (3)compute the transaction cost metric based on the computed values foreach option in the strip of K options.

According to other embodiments, the present invention is directed to acomputer-implemented method for computing a transaction cost metric fora trade order involving a tradable financial product. The method maycomprise: (1) computing, by a programmable computer system, a number ofcomplimentary orders K required to complete the trade order based on anotional size N for the trade order, wherein K≧1; (2) computing, by theprogrammable computer system, values for each option in a strip of Koptions using an option pricing formula, wherein each of the K optionshas a different tenor, and wherein respective tenors for each of the Koptions in the strip correspond to expected waiting times for each ofthe number of complimentary orders K required to fill the trade order;and (3) computing, by the programmable computer system, the transactioncost metric based on the computed values for each option in the strip ofK options.

According to other embodiments, the present invention is directed to acomputer readable medium having stored thereon instructions that, whenexecuted by a processor, cause the processor to: (1) compute a number ofcomplimentary orders K required to complete the trade order based on anotional size N for the trade order, wherein K≧1; (2) compute values foreach option in a strip of K options using an option pricing formula,wherein each of the K options has a different tenor, and whereinrespective tenors for each of the K options in the strip correspond toexpected waiting times for each of the number of complimentary orders Krequired to fill the trade order; and (3) compute the transaction costmetric based on the computed values for each option in the strip of Koptions.

According to various implementations, the tradable financial productcomprises a FX currency pair. Also, the transaction cost metric may bereferenced to a mid-price for the financial product at trade orderinception. In addition, computing the transaction cost metric maycomprise computing the transaction cost metric as an average of thecomputed values for each option in the strip of K options. Also, thetenors for each option in the strip of K options may be computed. Thetenors may be computed by, for each k, where k=1, 2, . . . , K, dividingk by an average rate of order arrival per unit time to determine thetenor for the k th option in the strip of K options comprises. Theoption pricing formula may use a strike price and a spot price for eachoption in computing the value for the option, and the strike price maybe an inside price for the financial product at order inception. Thespot price may be a mid-price for the financial product at orderinception. Also, a volatility for the financial product may be computed,where the computed volatility is used in the option pricing formula tocompute the values for the options in the strip.

Reference throughout the specification to “various embodiments,” “someembodiments,” “one embodiment,” “an embodiment,” and the like means thata particular feature, structure, or characteristic described inconnection with the embodiment is included in at least one embodiment.Thus, appearances of the phrases “in various embodiments,” “in someembodiments,” “in one embodiment,” “in an embodiment,” and the like inplaces throughout the specification are not necessarily all referring tothe same embodiment. Furthermore, the particular features, structures,or characteristics may be combined in any suitable manner in one or moreembodiments. Thus, the particular features, structures, orcharacteristics illustrated or described in connection with oneembodiment may be combined, in whole or in part, with the featuresstructures, or characteristics of one or more other embodiments withoutlimitation.

The examples presented herein are intended to illustrate potential andspecific implementations of the embodiments. It can be appreciated thatthe examples are intended primarily for purposes of illustration forthose skilled in the art. No particular aspect or aspects of theexamples is/are intended to limit the scope of the describedembodiments. The figures and descriptions of the embodiments have beensimplified to illustrate elements that are relevant for a clearunderstanding of the embodiments, while eliminating, for purposes ofclarity, other elements.

While various embodiments have been described herein, it should beapparent that various modifications, alterations, and adaptations tothose embodiments may occur to persons skilled in the art withattainment of at least some of the advantages. The disclosed embodimentsare therefore intended to include all such modifications, alterations,and adaptations without departing from the scope of the embodiments asset forth herein.

What is claimed is:
 1. A computer system for computing a transactioncost metric for a trade order involving a tradable financial product,the computer system comprising: at least one processor; and at least onememory unit in communication with the at least one processor, whereinthe at least one memory unit stores instructions that when executed bythe at least one processor cause the at least one processor to: computea number of complimentary orders K required to complete the trade orderbased on a notional size N for the trade order, wherein K≧1; computevalues for each option in a strip of K options using an option pricingformula, wherein each of the K options has a different tenor, andwherein respective tenors for each of the K options in the stripcorrespond to expected waiting times for each of the number ofcomplimentary orders K required to fill the trade order; and compute thetransaction cost metric based on the computed values for each option inthe strip of K options.
 2. The computer system of claim 1, wherein thetransaction cost metric is referenced to a mid-price for the financialproduct at trade order inception.
 3. The computer system of claim 1,wherein the at least one processor is further programmed to compute thetransaction cost metric based on an average of the computed values foreach option in the strip of K options.
 4. The computer system of claim1, wherein the at least one processor is further programmed to computethe tenors for each option in the strip of K options.
 5. The computersystem of claim 4, wherein the at least one processor is furtherprogrammed to compute the tenors for each option in the strip of Koptions by, for each k, where k=1, 2, . . . , K, dividing k by anaverage rate of order arrival per unit time to determine the tenor forthe kth option in the strip of K options comprises.
 6. The computersystem of claim 1, wherein the option pricing formula uses a strikeprice and a spot price, and wherein, for each of the K options, thestrike price is an inside price for the financial product at orderinception.
 7. The computer system of claim 6, wherein the spot price isa mid-price for the financial product at order inception.
 8. Thecomputer system of claim 7, wherein the at least one processor isfurther programmed to compute a volatility for the financial product,wherein the computed volatility is used in the option pricing formula tocompute the values for the options in the strip.
 9. The computer systemof claim 8, wherein the volatility comprises a range implied volatility.10. The computer system of claim 1, wherein the tradable financialproduct comprises an FX currency pair.
 11. A method for computing atransaction cost metric for a trade order involving a tradable financialproduct, the method comprising: computing, by a programmable computersystem, a number of complimentary orders K required to complete thetrade order based on a notional size N for the trade order, wherein K≧1;computing, by the programmable computer system, values for each optionin a strip of K options using an option pricing formula, wherein each ofthe K options has a different tenor, and wherein respective tenors foreach of the K options in the strip correspond to expected waiting timesfor each of the number of complimentary orders K required to fill thetrade order; and computing, by the programmable computer system, thetransaction cost metric based on the computed values for each option inthe strip of K options.
 12. The method of claim 11, wherein thetransaction cost metric is referenced to a mid-price for the financialproduct at trade order inception.
 13. The method of claim 11, whereincomputing the transaction cost metric comprises computing thetransaction cost metric as an average of the computed values for eachoption in the strip of K options.
 14. The method of claim 11, furthercomprising computing the tenors for each option in the strip of Koptions.
 15. The method of claim 14, wherein computing the tenors foreach option in the strip of K options comprises, for each k, where k=1,2, . . . , K, dividing k by an average rate of order arrival per unittime to determine the tenor for the kth option in the strip of K optionscomprises.
 16. The method of claim 11, wherein the option pricingformula uses a strike price and a spot price, and wherein, for each ofthe K options, the strike price is an inside price for the financialproduct at order inception.
 17. The method of claim 16, wherein the spotprice is a mid-price for the financial product at order inception. 18.The method of claim 17, further comprising computing, by theprogrammable computer system, a volatility for the financial, product,wherein the computed volatility is used in the option pricing formula tocompute the values for the options in the strip.
 19. The method of claim18, wherein the volatility comprises a range implied volatility.
 20. Acomputer readable medium having stored thereon instructions that, whenexecuted by a processor, cause the processor to: compute a number ofcomplimentary orders K required to complete the trade order based on anotional size N for the trade order, wherein K≧1; compute values foreach option in a strip of K options using an option pricing formula,wherein each of the K options has a different tenor, and whereinrespective tenors for each of the K options in the strip correspond toexpected waiting times for each of the number of complimentary orders Krequired to fill the trade order; and compute the transaction costmetric based on the computed values for each option in the strip of Koptions.
 21. The computer readable medium of claim 20, wherein thetransaction cost metric is referenced to a mid-price for the financialproduct at trade order inception.
 22. The computer readable medium ofclaim 20, wherein computing the transaction cost metric comprisescomputing the transaction cost metric as an average of the computedvalues for each option in the strip of K options.
 23. The computerreadable medium of claim 20, having further stored thereon instructionsthat when executed cause the processor to compute the tenors for eachoption in the strip of K options.
 24. The computer readable medium ofclaim 23, wherein computing the tenors for each option in the strip of Koptions comprises, for each k, where k=1, 2, . . . , K, dividing k by anaverage rate of order arrival per unit time to determine the tenor forthe kth option in the strip of K options comprises.
 25. The computerreadable medium of claim 20, wherein the option pricing formula uses astrike price and a spot price, and wherein, for each of the K options,the strike price is an inside price for the financial product at orderinception.
 26. The computer readable medium of claim 25, wherein thespot price is a mid-price for the financial product at order inception.27. The computer readable medium of claim 26, having further storedthereon instructions that when executed cause the processor to compute avolatility for the financial product, wherein the computed volatility isused in the option pricing formula to compute the values for the optionsin the strip.